7

Set 12: Linear Functions (Advanced)

Explanation

Answer: A

Which equation represents the line shown in the graph with a y-intercept of 3 and an x-intercept of -3?

A.

y=x+3y = x + 3

✓ Correct
B.

y=x+3y = -x + 3

C.

y=x3y = x - 3

D.

y=3x+3y = 3x + 3

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Find the slope from the intercepts. 1. Points: (0,3)(0, 3) and (3,0)(-3, 0). 2. Slope: m=0330=33=1m = \frac{0 - 3}{-3 - 0} = \frac{-3}{-3} = 1. 3. Y-intercept: b=3b = 3. 4. Equation: y=1x+3y = 1 x + 3, or y=x+3y = x + 3. Strategic Tip: A line crossing at (a,0)(a, 0) and (0,a)(0, a) always has a slope of 1 if signs match, or -1 if signs differ. Choice B is incorrect because it has a negative slope. Choice C is incorrect because it has the wrong y-intercept. Choice D is incorrect because it has the wrong slope.

Key Steps:

The correct answer is y=x+3y = x + 3

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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